Uncertainty in phase-frequency synchronization of large populations of globally coupled nonlinear oscillators

Numerical evidence as well as an analytical description is given for the existence of a kind of “uncertainty principle” in the mean-field model (of the Kuramoto type) of large populations of nonlinearly coupled oscillators. Here the noise plays the role of the Planck constant. This means that there is a limit to the possibility of synchronizing both, phases and frequencies. The collective phase synchronization competes in fact, within such a model, with the frequency synchronization. The explanation rests on the effect of the noise, which is responsible for loss of accuracy. Comparison is made with a more sophisticated model, where such uncertainty is absent when the coupling parameter is sufficiently large.